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A spectral method for Faraday waves in rectangular tanks


Horsley, DE and Forbes, LK, A spectral method for Faraday waves in rectangular tanks, Journal of Engineering Mathematics, 79, (1) pp. 13-33. ISSN 0022-0833 (2012) [Refereed Article]

Copyright Statement

Copyright 2012 Springer Science+Business Media B.V.

DOI: doi:10.1007/s10665-012-9562-0


A theoretical study of Faraday waves in an ideal fluid is presented. A novel spectral technique is used to solve the nonlinear boundary conditions, reducing the system to a set of nonlinear ordinary differential equations for a set of Fourier coefficients. A simple weakly nonlinear theory is derived from this solution and found to capture adequately the behaviour of the system. Results for resonance in the full nonlinear system are explored in various depth regimes. Time-periodic solutions about the main (subharmonic) resonance are also studied in both the full and weakly nonlinear theories, and their stability calculated using Floquet theory. These are found to undergo several bifurcations which give rise to chaos for appropriate parameter values. The system is also considered with an additional damping term in order to emulate some effects of viscosity. This is found to combine the two branches of the periodic solutions of a particular mode.

Item Details

Item Type:Refereed Article
Keywords:Faraday waves, Floquet stability analysis, inviscid fluid, nonlinear resonance
Research Division:Engineering
Research Group:Fluid mechanics and thermal engineering
Research Field:Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Horsley, DE (Dr David Horsley)
UTAS Author:Forbes, LK (Professor Larry Forbes)
ID Code:79948
Year Published:2012
Web of Science® Times Cited:11
Deposited By:Mathematics and Physics
Deposited On:2012-10-15
Last Modified:2015-01-27

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